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Further Mathematics
A Level

Find the general solution to y''+2y'-3y=x

y''=d2y/dx2, y'=dy/dx for ease of writing

First off split the full equation into th homogeneous equation and the particular function. 

The homogen...

ZG
7079 Views

Find the first three non-zero terms of the Taylor series for f(x) = tan(x).

We have that the Taylor series of a function infinitely differentiable at a x = a is given by the expansion: f(x) = f(a) + f'(a)(x - a) + f''(a

AS
10886 Views

The quadratic equation x^2-6x+14=0 has roots alpha and beta. a) Write down the value of alpha+beta and the value of alpha*beta. b) Find a quadratic equation, with integer coefficients which has roots alpha/beta and beta/alpha.

a) We know that, for a general quadratic equation that can be written as : ax2+bx+c=0, the sum of its roots (S) is equal to -b/a and the product of its roots (P...

BC
25519 Views

A useful practice: how to determine the number of solutions of a system of linear equations beforehand

We have a system of n linear equations incorporated by Ax = b, with being a n x p matrix of numeric coefficients, x being a p-dime...

FB
2915 Views

Find the determinant of a 3x3 matrix.

Will need a whiteboard so I can draw a matrix to fully explain.

SM
2293 Views

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